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{\bf Question}

Write down the sum ${\bf{a}}+{\bf{b}}$ and difference
${\bf{a}}-{\bf{b}}$ of the vectors:

\begin{description}
\item[(i)]
${\bf{a}}=3{\bf{i}}-2{\bf{j}}+{\bf{k}}\
{\bf{b}}=-{\bf{i}}-2{\bf{j}}+3{\bf{k}}$

\item[(ii)]
${\bf{a}}=-{\bf{i}}+2{\bf{j}}-{\bf{k}},\
{\bf{b}}=2{\bf{i}}-4{\bf{j}}+2{\bf{k}}$
\end{description}
\medskip

{\bf Answer}
\begin{description}
\item[(i)]
${\bf{a}}+{\bf{b}}=3{\bf{i}}-2{\bf{j}}+{\bf{k}}-
{\bf{i}}-2{\bf{j}}+3{\bf{k}}=2{\bf{i}}-4{\bf{j}}+4{\bf{k}}$

${\bf{a}}-{\bf{b}}=3{\bf{i}}-2{\bf{j}}+{\bf{k}}-(-{\bf{i}}-
2{\bf{j}}+3{\bf{k}})=4{\bf{i}}-2{\bf{k}}$

\item[(ii)]
${\bf{a}}+{\bf{b}}=-{\bf{i}}+2{\bf{j}}-{\bf{k}}+2{\bf{i}}
-4{\bf{j}}+2{\bf{k}}={\bf{i}}-2{\bf{j}}+{\bf{k}}$

${\bf{a}}-{\bf{b}}=-{\bf{i}}+2{\bf{j}}-{\bf{k}}-(2{\bf{i}}
-4{\bf{j}}+2{\bf{k}})=-3{\bf{i}}+6{\bf{j}}-3{\bf{k}}$
\end{description}
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